Semiclassical theory of speckle correlations

Abstract

Coherent wave propagation in random media results in a characteristic speckle pattern, with spatial intensity correlations with short-range and long-range behavior. Here, we show how the speckle correlation function can be obtained from a ray picture for two representative geometries, namely a chaotic cavity and a random waveguide. Our calculation allows us to study the crossover between a “ray limit” and a “wave limit,” in which the Ehrenfest time τE is larger or smaller than the typical transmission time τD, respectively. Remarkably, long-range speckle correlations persist in the ray limit τE≫τD.